The geometric cobordism hypothesis

--- lecture course by Daniel Grady and Dmitri Pavlov, July 4-8, 2022, daily at 4:00-5:30 pm UTC+2 ---


Abstract:
We will explain our recent work on locality of functorial field theories (arXiv:2011.01208) and the geometric cobordism hypothesis (arXiv:2111.01095). The latter generalizes the Baez-Dolan cobordism hypothesis to nontopological field theories, in which bordisms can be equipped with geometric structures, such as smooth maps to a fixed target manifold, Riemannian metrics, conformal structures, principal bundles with connection, or geometric string structures. Applications include a generalization of the Galatius-Madsen-Tillmann-Weiss theorem, a solution to a conjecture of Stolz and Teichner on representability of concordance classes of functorial field theories, and a construction of power operations on the level of field theories (extending the recent work of Barthel-Berwick-Evans-Stapleton).

Registration:
If you would like to participate, please send an informal registration email to nils.carqueville@univie.ac.at.

Slides and Recordings:
Lecture 1: Introduction (by Dmitri Pavlov: slides, video)
Lecture 2: Definitions (by Daniel Grady: slides, video)
Lecture 3: Locality (by Dmitri Pavlov: slides, video)
Lecture 4: The geometrically framed case (by Daniel Grady: slides, video)
Lecture 5: Leftovers and examples (by Daniel Grady and Dmitri Pavlov: slides 1, slides 2, video)

Organisation:
Domenico Fiorenza, Konrad Waldorf, Nils Carqueville